Recrusive formula for z-function in TS/KMN starting conditions does not match actual

jrenaud90 / TidalPy

Software suite to perform solid-body tidal dissipation calculations for rocky and icy worlds

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Recrusive formula for z-function in TS/KMN starting conditions does not match actual #42

Open jrenaud90 opened 9 months ago

jrenaud90 commented 9 months ago

The recrusision formula shown in TS72 and KMN15 (See TS72 Eq. 97) does not reproduce the full version of this function (TS72 Eq. 96). I am finding it to be off by about 30% at l = 2 and then the error improves to 10% at l=10. Perhaps thre is a problem with the implementation.

For this reason, for now, TidalPy does not use this recrusive formula (see cf_z_calc in "RadialSolver.starting.common.pyx").